Answer
(a) If we triple the radius, then the circumference increases by a factor of 3.
(b) If we triple the radius, then the area increases by a factor of 9.
Work Step by Step
(a) Let $r$ be the original radius of the circle.
The circumference is $C_1 = 2\pi r$
If we triple the radius, then the new radius is $3r$
The new circumference is $C_2 = 2\pi (3r) = 3\times 2\pi r = 3\times C_1$
If we triple the radius, then the circumference increases by a factor of 3.
(b) Let $r$ be the original radius of the circle.
The area is $A_1 = \pi r^2$
If we triple the radius, then the new radius is $3r$
The new area is $A_2 = \pi (3r)^2 = 9\times \pi r^2 = 9\times A_1$
If we triple the radius, then the area increases by a factor of 9.
